Question

How to use the discriminant to find out what type of solutions the equation has for `3z^2 + z - 1 = 0`?

Answer 1

`3z^2+z-1` is of the form `az^2+bz+c`, with `a=3`, `b=1` and `c=-1`.

The discriminant is given by the formula:

`Delta = b^2-4ac = 1^2-(4xx3xx-1) = 1+12 = 13`

Since `Delta > 0`, the quadratic has two distinct real roots. However, `Delta` is not a perfect square, so those roots are irrational (involving `sqrt(13)`).